Bring 1 cup coconut milk, lemon grass, ginger, and kaffir lime leaves to a boil in a large skillet over medium-high heat. Stir in the chicken, fish sauce, and sugar. Reduce heat to medium, and continue cooking until the chicken no longer pink in the center, about 5 minutes. Stir in the remaining 1 cup coconut milk, and bring to a simmer, about 3 minutes.
Divide the lime juice and curry paste into 4 bowls. Pour soup into bowls, and garnish with cilantro and Thai chiles.